profit and loss

Question

A trader sells a type of sugar for Rs. 60 per kg at a loss of 20% and another sugar at Rs. Selling 100 per kg makes 25% profit. He mixed the two results equally and gave the mixture Rs. Sold at 120 per kg. What is his profit percentage now?

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Answer 1

Let's assume the trader initially had 1 kg of each type of sugar.

For the first type of sugar:
Selling price = Rs. 60 per kg
Loss = 20%

The cost price (CP) for the first sugar is calculated as follows:
CP = Selling price / (1 - Loss %)
CP = 60 / (1 - 0.20)
CP = 60 / 0.80
CP = Rs. 75 per kg

For the second type of sugar:
Selling price = Rs. 100 per kg
Profit = 25%

The cost price (CP) for the second sugar is calculated as follows:
CP = Selling price / (1 + Profit %)
CP = 100 / (1 + 0.25)
CP = 100 / 1.25
CP = Rs. 80 per kg

Now, the trader mixes the two types of sugar equally. So, for 1 kg of the mixture, the total cost price (TCP) would be:
TCP = (CP of first sugar + CP of second sugar) / 2
TCP = (75 + 80) / 2
TCP = 155 / 2
TCP = Rs. 77.50

The trader sells this mixture at Rs. 120 per kg, resulting in a selling price of Rs. 120 per kg.

Profit = Selling price - Cost price
Profit = 120 - 77.50
Profit = Rs. 42.50

To find the profit percentage, we use the formula:
Profit percentage = (Profit / Cost price) * 100

Profit percentage = (42.50 / 77.50) * 100
Profit percentage ≈ 54.84%